Geometric deformation correction method and system for dot pattern images

ABSTRACT

A method and system for correcting geometric deformations in an aligned image. A shape deformation correction unit is provided for receiving the aligned image and based thereon for generating a shape-corrected image. A space deformation correction unit is coupled to the shape deformation correction unit and receives the shape-corrected image. The space deformation correction unit uses the shape-corrected image to generate edges and interfaces, and further generates a corrected image based on the interfaces and the shape-corrected image.

FIELD OF THE INVENTION

The present invention relates generally to image processing and morespecifically to a geometric deformation correction method and system fordot pattern images.

BACKGROUND OF THE INVENTION

Bar-codes are information carrying graphical patterns designed for easyand reliable automatic retrieval. The most common bar-codes are known asone-dimensional bar-codes. These graphical patterns vary in a singledimension (e.g. the horizontal dimension), and are constant in the otherdimension (e.g., the vertical dimension). One-dimensional bar-codes areemployed in low information content applications like product indexregistry (e.g. automatic price tagging and inventory management), orserial number registry (e.g. test-tube tagging in automated medicaltests). Common examples of one-dimensional bar-codes are those bar-codesthat are affixed or printed on the packages of items purchased at asupermarket or other store. These bar-codes typically can only encodelimited information, such as the price of the item and the manufacturer.The items having the bar-codes are scanned at a checkout counter tofacilitate the tallying up of a total receipt.

In order to convey more information on the same surface area,two-dimensional bar-codes were developed. Two-dimensional bar-codesinvolve intricate patterns that vary in both the horizontal and thevertical dimensions. Two-dimensional bar-codes are used in applicationsthat require more information content. For example, two-dimensionalbar-codes can be used to encode mail addresses for automated mailreading and distribution systems. Mail carrier companies can use thetwo-dimensional bar code on shipping packages to encode shipperinformation, recipient information, tracking information, etc. Inanother example, two-dimensional bar-codes can be used to encode thecompressed content of a printed page to avoid the need for opticalcharacter recognition at the receiving end.

Two-dimensional bar-codes are typically graphical patterns composed ofdots that are rendered by using two-toned dots (e.g. black dots on awhite background). These dots usually occupy a rectangular area. Mostcurrent systems use a bar-code printer to print an original bar-code,and the bar-code readers detect that original bar-code. However, it isdesirable in many office applications to have a bar-code system that canscan and reliably recover information from copies of the originalbar-code. For example, if the original bar-code is embedded in an officedocument and is given to a first worker, and the first worker desires toshare the document with a co-worker, it would be desirable for the firstworker to copy the document and provide the same to the co-worker havingconfidence that the information embedded in a bar-code in the documentcould be recovered by the co-worker if needed.

Unfortunately, the prior art bar-code and bar-code reading systemscannot reliably recover information encoded in the bar-code except froman original bar-code that is newly printed by a bar-code printer. Forexample, most systems have difficulty in reliably reading and recoveringinformation from a bar-code that is a photocopy of the original.Moreover, prior art systems have an even greater difficulty inaccurately reading and recovering information from a bar-code that is aphotocopy of another photocopy of the bar-code (e.g., a bar-code thathas been photocopied two or more times).

Accordingly, a challenge in the design of 2D bar-codes and systems toread such bar-codes is to develop a scheme that can produce bar-codesand reliably recover information from bar-codes, even after successivecopies of the original, using office equipment. In other words, thesystem needs to be designed in such a way as to compensate fordegradation of the bar-code, thereby making such a system robust. Insummary, it is desirable that a bar-code design and bar-code system bedesigned in such a way as to ensure that the bar-codes can be recognizedand the encoded information recovered even after successive copying andhandling in a paper path.

The bar-code pattern is often degraded between the time of creation andits use. These degradations can include contrast reduction, stains,marks, and deformations. Many degradations can be corrected by utilizingone or more traditional methods, such as contrast enhancement, adaptivethresholding, and error-correction coding. However, geometric patterndeformation remains a challenge and does not lend itself to resolutionby prior art methods. Geometric pattern deformation can occur, forexample, when a pattern is photocopied.

The photocopying process can inject the following types of geometricdeformations to the dots in a bar-code pattern. The first type ofgeometric deformations is shape deformations. Shape deformations causethe dots to change their size either shrinking or expanding the dots.Shape deformations typically depend on the brightness setting of thecopier. For example, when the brightness setting is set to a darkersetting, the dots tend to expand. When the brightness setting is set toa lighter setting, the dots tend to shrink.

The second type of geometric deformations is space deformations. Spacedeformations cause the dots corresponding to certain coordinates in theoriginal image to be located at different coordinates in the copy. Thereare two types of space deformations: global deformations and localdeformations. Global shape deformations, such as translation, rotationor affine, are those that change the coordinates of the dots in a waythat is consistent with an equation that describes the deformations forthe entire image. There are also local space deformations that aredeformations that cannot be modeled as a global space deformation. Theselocal space deformations are especially difficult to characterize andcorrect.

Accordingly, there remains a need for a method for correcting geometricdeformations in bar-code patterns that overcomes the disadvantages setforth previously.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a method forcorrecting geometric deformations in a bar-code pattern.

It is another object of the present invention to provide a method forcorrecting shape deformations in a bar-code pattern.

It is a further object of the present invention to provide a method forcorrecting space deformations in a bar-code pattern.

A method and system for correcting geometric deformations in an alignedimage. A shape deformation correction unit is provided for receiving thealigned image and based thereon for generating a shape-corrected image.A space deformation correction unit is coupled to the shape deformationcorrection unit and receives the shape-corrected image. The spacedeformation correction unit uses the shape-corrected image to generateedges and interfaces, and further generates a corrected image based onthe interfaces and the shape-corrected image.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings and in whichlike reference numerals refer to similar elements.

FIG. 1 illustrates a bar-code decoding system in which the geometricdeformation correction unit of the present invention can be implemented.

FIG. 2 illustrates in greater detail the geometric deformationcorrection unit of FIG. 1 configured according to one embodiment of thepresent invention.

FIG. 3 is a flowchart illustrating a method for correcting geometricdeformation in patterns in accordance with one embodiment of the presentinvention.

FIG. 4 is an exemplary structuring element that can be utilized forshape deformation correction in accordance with one embodiment of thepresent invention.

FIG. 5 illustrates how the present invention corrects shape deformationin an exemplary dot pattern image.

FIG. 6 illustrates how the present invention corrects space deformationin an exemplary dot pattern image.

DETAILED DESCRIPTION

In the following description, for the purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of the present invention. It will be apparent, however, toone skilled in the art that the present invention may be practicedwithout these specific details. In other instances, well-knownstructures and devices are shown in block diagram form in order to avoidunnecessarily obscuring the present invention. The following descriptionand the drawings are illustrative of the invention and are not to beconstrued as limiting the invention.

As described previously, an image is typically rendered using two tones(e.g., black dots on a white background).

Bar-code Decoding System 10

FIG. 1 illustrates a bar code decoding system 10 configured inaccordance with one embodiment of the present invention. The bar codedecoding system 10 includes a pre-processing unit 12 for receiving ascanned image 13 (e.g., an image that has been distorted throughsuccessive copying) and for performing pre-processing operations and forcorrecting global shape deformations in the scanned image 13 throughenhancement and alignment operations to generate an aligned image 15.For example, global space deformations are corrected by thepre-processing unit 12. As described previously, global shapedeformations, such as translation, rotation or affine, are those thatchange the coordinates of the dots in a way that is consistent with anequation that describes the deformations for the entire image. Globalspace deformations may be corrected by determining one or moreparameters (e.g., translation vector or rotation angle) that model theglobal deformation.

The bar code decoding system 10 also has a geometric deformationcorrection unit 14 that is coupled to the pre-processing unit 12 forreceiving the aligned image 15 and for correcting deformations in thealigned image 15 to generate a corrected image 17. The geometricdeformation correction unit 14 also optionally includes a second inputfor receiving one of more reference features 11 (e.g., the average graylevel or dot size of the original image) that can be utilized to correctdeformations in the aligned image 15.

The bar code decoding system 10 also has a graphic demodulation anddecoding unit 16 that is coupled to the geometric deformation correctionunit 14 for receiving the corrected image 17 and for recoveringinformation 19 (e.g., information encoded in a two-dimensional bar code)from the corrected image 17. Demodulation and decoding operations arewell known by those of ordinary skill in the art and will not bedescribed in greater detail herein.

FIG. 2 illustrates in greater detail the geometric deformationcorrection unit 14 of FIG. 1 configured according to one embodiment ofthe present invention. The geometric deformation correction unit 14includes a shape-deformation correction unit 30 for correcting shapedeformations in the aligned image 15, and a space-deformation correctionunit 34 for correcting space deformations in the shape-corrected image47 generated by the shape-deformation correction unit 30.

The shape-deformation correction unit 30 includes a distortion measuredetermination unit 40 and a dot size modification unit 44. Thedistortion measure determination unit 40 receives the aligned image 15and based thereon determines the distortion measure 41 of the alignedimage 15. Preferably, the distortion measure determination unit 40 alsoreceives one or more features 11 of a reference image (e.g., one or morefeatures of the original image) and uses those features to determine thedistortion measure 41. The dot size modification unit 44 that is coupledto distortion measure determination unit 40 receives the aligned image15 and the distortion measure 41 and performs shape deformationcorrection on the aligned image 15 based on the distortion measure 41 togenerate a shape-corrected image 47. The terms, “dot or “dots,” as usedherein, refers to any objects that are used to render an imageregardless of actual shape. For example, the dots can have a rectangularshape or any other geometric shape.

The present invention insures that the image rendered with dot patternsand any information encoded therein are preserved even after successivecopies of the original image.

The space-deformation correction unit 34 includes a directed edgedetection unit 50 for generating edges 52, an interface detection unit54 for generating interfaces 56 based on the edges 52, and a dotalignment unit 58 for performing space-deformation correction on theshape-corrected image based on the interfaces 56 to generate a correctedimage 17.

FIG. 3 is a flowchart illustrating the steps of a method of geometricdeformation correction in accordance with one embodiment of the presentinvention. First, at least one morphological operation is utilized tocorrect for shape deformations. Preferably, the shape deformations aremodeled as a morphological dilation or erosion of the black pattern,which are then corrected by the present invention by erosion ordilation, respectively. Second, row/column gradient statistics areutilized to correct for local, approximately-separable, spacedeformations. A separable space deformation is when all dots in a columnmove the same amount in the horizontal direction, and all dots in a rowmove the same amount in the vertical direction so that the deformationof each dot can be deduced from its position. The term “approximatelyseparable deformation” refers to deformations with a negligible amountof movement that cannot be explained by the separable model.

In step 300, the distortion measure determination unit 40 determines adistortion measure (e.g., a shape deformation measure) that reflects theextent to which portions of the pattern (e.g., the black dots) haveeroded or expanded relative to the original pattern. As will beexplained hereinafter, this step can be performed with or withoututilizing one or more reference features 11.

In an exemplary implementation of step 300, the following steps areperformed. First, an average tone or darkness of the aligned pattern iscalculated. Next, an average tone or darkness of a reference pattern(e.g., the original pattern) is calculated. The average tone of thealigned pattern is then compared with the average tone of the referencepattern, and a tone difference is generated. The tone difference is thenutilized to generate a shape deformation measure, which in one example,is an erosion radius or a dilation radius.

In general, the relative area of the black pattern in a visuallysignificant bar-code is equal to the average gray value of the originalimage (i.e., the image that the bar-code renders). Accordingly, thefollowing specific steps may be performed for determining the distortionmeasure. First, the aligned image is binarized using a thresholdfunction, and the relative area, b, of the black part is compared to theaverage gray value, g, of the original image. If the relative area, b,is smaller than the average gray value, g, the required morphologicaloperation is dilation of the black dots. On the other hand, if therelative area, b, is larger than the average gray value, g, the requiredmorphological operation is erosion of the black dots. The radius, r, ofthe required morphological correction is a function of the absolutedifference |g−b|. In one embodiment, this function may be approximatedas a linear function: r=9|g−b|, where b and g are represented asfractions in the range [0, 1].

In an alternative exemplary implementation of step 300, an averageapproach performs the following steps. First, single dots in the alignedpattern are located. Second, information, such as an average gray levelor dot size, is received. Next, the radius of the single dots in thealigned pattern is then compared to the information, and a shapedeformation measure is generated based on this comparison.Alternatively, the radius of a single white dot may be compared to theradius of a single black dot in the aligned image, and a shapedeformation measure may be generated based on this comparison withoutusing information from the original pattern or other referenceinformation (e.g., average gray value or dot size).

This approach first applies a super-resolution edge-detection method,which is well known to those of ordinary skill in the art, on thedeformed dot shapes. Next, horizontal and vertical black runs aremeasured. Runs originating in n dots are measured n·R+2r, where R is thedot radius, and r the deformation radius. Then, the deformation radius ris calculated by determining the radius that minimizes the best robustsquare fit of the measurements to the above model. For an example ofthis approach, please refer to Carl Staelin, and Larry McVoy, “mhz:Anatomy of a micro-benchmark”, in Proceedings of USENIX 1998 AnnualTechnical Conference, pp. 155, New Orleans, La., June 1998.

In step 304, a dot size modification unit 44 generates a shape-correctimage 47 based on aligned image 15 and the distortion measure 41.Preferably, the dot size modification unit 44 selectively modifies thesize of the dots to compensate for the respective expansion or shrinkagethereof caused by the shape deformation. Step 304 may be implemented byutilizing at least one morphological operation that either erodes ordilates a dot pattern with a specified shape deformation measure (e.g.,a specified radius). It is noted that the dot size modification unit 44is not limited to a module that changes the size of dots in an image,but instead can be any unit that compensates for shape deformation of animage by using a distortion measure.

Referring to FIG. 4, the present invention preferably utilizes astructuring element having a cross shape. The element includes entries:b₀ in the center, b₁ in coordinates (±1,0) and (0,±1), b₂ in coordinates(±2,0) and (0,±2), and so on.

The shape compensation unit 44 generates a corrected image by performinga morphological gray scale dilation or erosion of the image with theabove structuring element. In other words, the shape compensation unit44 places the structuring element on every pixel in the input image.Then, the value of the dilation at the corresponding pixel is determinedby calculating the minimum of the sums of neighboring pixel values withthe structuring-element values placed on them. For erosion one simplytakes the maximum of differences:${Dilate}_{i,j} = {{\underset{{k.l} \in {SE}}{Min}\left\{ {I_{{i + k},{j + l}} + S_{{k,l}\quad}} \right\} \quad {and}\quad {Erode}_{i,j}} = {\underset{k,{l \in {SE}}}{Max}\left\{ {I_{{i + k},{j + l}} - S_{k,l}} \right\}}}$

where SE is the set of valid structuring-element coordinates, andI_(m,n), S_(m,n) are image and structuring-element values at coordinates(m,n). (S_(k,l) obtains one of b₀,b₁,b₂, . . . ).

The values b₀,b₁,b₂, . . . should be such that they perform as astructuring element of a given radius. For integer valued radii thefollowing can be used:$\rho = {\left. i\Rightarrow b_{j} \right. = \left\{ \begin{matrix}0 & {for} & {j \leq i} \\1 & {for} & {j > i}\end{matrix} \right.}$

For non-integer radii, the following transformation can be used:${\rho \in \left. \left\lbrack {{i - 1},i} \right\rbrack\Rightarrow b_{j} \right.} = \left\{ \begin{matrix}0 & {for} & {j < i} \\{0.22 \cdot \left( {i - \rho} \right)} & {for} & {j = i} \\1 & {for} & {j < i}\end{matrix} \right.$

which was found to give a linear correction in terms of the distortionmeasure (e.g., deformation radius) as measured by the distortion measuredetermination unit 40. For example, if an image with a measureddeformation radius of r₀, is corrected with radius −r₁, the subsequentdeformation radius will measure r₀−r₁.

Alternatively, step 304 can be implemented by modifying thepredetermined threshold that defines a black pattern in the alignedimage. Specifically, the threshold defining the black pattern ismodified by the shape compensation unit 44. Since the black pattern isobtained from the aligned image by using a threshold, the shapecompensation unit 44 can modify the threshold, thereby modifying thearea of the black pattern.

In step 308, directed edge detection unit 50 detects edges (e.g.,horizontal edges and vertical edges). Preferably, the horizontal edgesare detected by performing a directed horizontal gradient estimation,and the vertical edges are detected by performing a directed verticalgradient estimation. For example, a forward derivative can be utilizedin the horizontal or vertical direction to estimate the directed edgesin the respective direction. It is noted that any directed edgedetection kernel can be utilized in this step.

Alternatively, the horizontal edges are detected by determining the zerocrossing of a directed horizontal Laplacian operation, and the verticaledges are detected by performing a directed vertical Laplacianoperation. The Laplacian operation and the determination of zerocrossing are well-known to those of ordinary skill in the imageprocessing art and will not be described herein.

In step 314, interface detection unit 54 determines the interfaces(e.g., dot-row interfaces and dot-column interfaces) based on edgeinformation 52 (e.g., horizontal edges and vertical edges). When thebar-code covers a relatively small area of the total area (e.g., acorner of a paper), the space deformation can be safely approximated asseparable. A separable space deformation is defined as the situation inwhich the row and column interfaces are aligned with pixel rows andcolumns, and the deformation is expressed only in the unevendistribution of the interfaces.

At column interfaces there are many transients between black dots on theright of the interface and white dots on the left, or vise versa.Accordingly, in order to find the column interfaces, the interfacedetection unit 54 sums the absolute values of horizontal gradients incolumns and locates the columns with high peaks in the gradient sum. Tofind the row interfaces, interface detection unit 54 simply transposesthe image and performs the same operation described above.Alternatively, the interface detection unit 54 sums the absolute valuesof vertical gradients in rows and locates the rows with high peaks inthe gradient sum.

In the preferred embodiment, the interface detection unit 54 alsoprovides for outlier interfaces. First, the interface detection unit 54determines a range (e.g. a range measured from the last interface) inwhich to look for the new interface. If no interface is detected in thatrange, the interface detection unit 54 determines the interface to be astandard dot-size away from the last interface. In this manner, outlierinterfaces are detected. Outlier interfaces are those which for somereason, have a weak gradient activity (e.g. a situation where in mostrows, dots on both sides of the interface have identical values).

Alternatively, the interface detection unit 54 performs the followingprocedure that is especially useful in applications where the spacedeformation is distinctly not separable. First, the interface detectionunit 54 estimates column interfaces row-by-row. In every row thelocation of each column interface is determined so as to satisfy one ormore consistency requirements.

These consistency requirements can include, but are not limited to: (1)the interface should preferably agree with local large gradientmagnitudes; (2) the interface should not deviate much from its locationin the previous row; and (3) the interface should form a quasi-uniformpattern with near by interface locations in the same row.

The following is an exemplary implementation of the above-describedalternative embodiment for the interface detection unit 54. First,interfaces are recorded in sub-pixel accuracy. Next, binary gradientsare determined by thresholding the aligned image. If a gradient islocated within a predetermined pixel distance (e.g., 1.5 pixel from aninterface location in the previous row, the gradient is associated withthat interface. Interfaces with no gradient association keep theirlocation from the previous row. Interfaces with multiple gradientassociations relate only to the closest gradient, and determine theirnew location as a weighted average between its location (e.g., weight of0.3) and their location in the previous line (e.g., weight of 0.7). Whenall the interfaces for a row have been determined this way, their finallocation is a weighted-average between these locations and the averagelocation of their respective neighbors on the left and right. It isnoted that the average extent may range up to several interfaces on eachside.

In step 318, the dot alignment unit 58 corrects space deformation in theshape-corrected image 47 based on the interfaces 56. In the preferredimplementation, the dot alignment unit 58 virtually aligns the dots byaugmenting the aligned image with a list of dot centers. The listdescribes a potentially non-uniform square grid of dot centers. The dotalignment unit 58 computes dot center coordinates as the center of theinterface coordinates on both sides.

Alternatively, the dot alignment unit 58 can compose a new image fromsub-images cropped around located dot centers. In this manner, dotcenters in the shape-corrected image 47 are located on a uniform squaregrid, and each dot covers a square patch of pixels around it. Thissquare patch is cropped out of the respective dot location in theshape-corrected image 47. In this approach, there are pixels in theshape-corrected image 47 that will not be found in the corrected image17, and other pixels that are copied to several locations in thecorrected image 17.

FIG. 5 illustrates how the present invention corrects shape deformationin an exemplary dot pattern image 500. The original dot pattern image500 has a plurality of black and white pixels (e.g., black and whitesquares) that are arranged in rows and columns. After successive copies,the pixels dilate and cross row and column interfaces. For example, acopied image 508 shows how the original pattern is deformed after fivecopies. It is readily apparent that the white pixels, for example, havedilated to cross row interface 540 after successive copies. The presentinvention utilizes the shape deformation correction unit 30 to receivethe copied image 508 and correct shape deformations to generate a shapecorrected image 530. It is noted that corrected image 530 features rowinterfaces and column interfaces that are better aligned than those ofthe copied image 508. Also, single dots are easier to determine in thecorrected image 530 than in the copied image 508.

FIG. 6 illustrates how the present invention corrects space deformationin an exemplary dot pattern image 600. The dot pattern image 600 hassixteen pixels arranged in rows and columns. In this example, there aretwo rows with each row having eight pixels. A first copy 610 shows howdots have undergone a separable deformation (e.g., when all the dots inthe first row have been moved an equal amount in the negative ydirection). Similarly, all the dots in the second row have alsoundergone a separable deformation in that they have been moved in anequal amount in the negative y direction. A second copy 620 shows dotsthat have undergone a non-separable deformation (e.g., when the movementof dots in the first row is independent and different for each dot inthe first row). Similarly, all the dots in the second row have alsoundergone a non-separable deformation in that the movement of dots inthe second row is independent and different for each dot in the secondrow. In either case, the present invention corrects for the spacedeformation by either measuring the coordinate deformation for the eachrow when the deformation is separable as in the case with the first copy610 or by measuring the coordinate deformation for each dot in each rowwhen the deformation is non-separable as in the case with the secondcopy 620. The present invention receives either the first copy 610 orthe second copy 620 and corrects the space deformations to generate acorrected image 630.

The foregoing description has provided numerous examples of the presentinvention. It will be appreciated that various modifications and changesmay be made thereto without departing from the broader scope of theinvention as set forth in the appended claims.

What is claimed is:
 1. A method for correcting geometric deformationscomprising: (a) receiving a aligned image having a plurality of dotsthat have undergone geometric deformation; (b) correcting the shapedeformations of the dots in the aligned image by utilizing at least onemorphological operation to generate a shape-corrected image; and (c)correcting the space deformation in the shape-corrected image byutilizing row/column gradient statistics to generate a corrected image.2. The method of claim 1 further comprising: determining an average toneof the aligned image; and generating a distortion measure based on theaverage tone of the aligned image.
 3. The method of claim 2 whereingenerating a distortion measure based on the average tone of the alignedimage comprises: generating one of a dilation radius and an erosionradius based on the average tone.
 4. The method of claim 1 furthercomprising: determining a dimension of a first dot in the aligned image;determining a dimension of a second dot in the aligned image; andgenerating a distortion measure based on the dimension of the first dotand the dimension of the second dot.
 5. The method of claim 4 whereindetermining a dimension of the first dot in the aligned image includesdetermining a radius of the first dot; wherein determining a dimensionof the second dot in the aligned image includes determining a radius ofthe second dot; and wherein generating a distortion measure based on thedimension of the first dot and the dimension of the second dot includesgenerating one of a dilation radius and an erosion radius based on thedimension of the first dot and the dimension of the second dot.
 6. Themethod of claim 1 wherein correcting the shape deformations of the dotsby utilizing at least one morphological operation includes: determininga distortion measure based on the aligned image; and modifying at leastone dimension of the dots based on the distortion measure.
 7. The methodof claim 1 wherein correcting the shape deformations of the dots byutilizing at least one morphological operation includes: determining adistortion measure based on the aligned image; and modifying a thresholdfor defining a black pattern in the aligned image.
 8. The method ofclaim 1 wherein correcting the space deformation by utilizing row/columngradient statistics includes: determining dot interfaces based on thealigned image; and adding dot center information to the aligned imagebased on the dot interfaces.
 9. The method of claim 8 whereindetermining dot interfaces based on the reference image and the alignedimage includes: detecting horizontal edges; locating dot-columninterfaces based on the horizontal edges; detecting vertical edges; andlocating dot-row interfaces based on the vertical edges.
 10. The methodof claim 9 wherein detecting horizontal edges includes detectinghorizontal edges by utilizing a directed horizontal gradient estimation,and wherein detecting vertical edges includes detecting vertical edgesby utilizing a directed vertical gradient estimation.
 11. The method ofclaim 9 wherein detecting horizontal edges includes detecting horizontaledges by determining the zero crossing of a directed horizontalLaplacian operation, and wherein detecting vertical edges includesdetecting vertical edges by determining the zero crossing of a directedvertical Laplacian operation.
 12. The method of claim 1 whereincorrecting the space deformation by utilizing row/column gradientstatistics includes: determining dot interfaces based on the alignedimage; determining dot centers based on the dot interfaces; generating anew image having a plurality of sub-images cropped around the dotcenters.
 13. The method of claim 1 further comprising: correctingseparable space deformations; wherein the step of correcting separablespace deformations includes locating dot-column interfaces by summingthe absolute value of the horizontal gradient in columns; wherein alarge sum indicates a dot-column interface; and locating dot-rowinterfaces summing the absolute value of the vertical gradient in therows; wherein a large sum indicates a dot-row interface.
 14. The methodof claim 1 further comprising: correcting non-separable spacedeformations; wherein the step of correcting non-separable spacedeformations includes estimating column interfaces row-by-row andrequiring consistency with gradient magnitudes, near by interfacelocations, and interface locations in a previous row.
 15. The method ofclaim 1 further comprising: correcting non-separable space deformations;wherein the step of correcting non-separable space deformations includesestimating row interfaces column-by-column and requiring consistencywith gradient magnitudes, near by interface locations, and interfacelocations in a previous column.
 16. The method of claim 1 furthercomprising: receiving a reference image; determining an average tone ofthe reference image; determining an average tone of the aligned image;comparing the average tone of the reference image and the average toneof the aligned image to generate a difference in tone; and generating adistortion measure based on the difference in tone.
 17. The method ofclaim 1 further comprising: receiving a reference image; determining adimension of a dot in the reference image; determining a dimension of acorresponding dot in the aligned image; comparing the dimension of a dotin the reference image and the dimension of a corresponding dot in thealigned image to generate a difference in dimension; and generating adistortion measure based on the difference in dimension.
 18. A geometricdeformation correction system comprising: a shape deformation correctionunit for receiving a aligned image and based thereon for generating ashape-corrected image; and a space deformation correction unit, coupledto the shape deformation correction unit, for receiving theshape-corrected image, generating edges and interfaces, and generatingan aligned image based on the interfaces and the shape-corrected image.19. The correction system of claim 18 wherein the shape deformationcorrection unit further comprises: a distortion measure determinationunit for receiving a reference image and generating a distortion measurethat represents the relative distortion between dots in a referenceimage and the aligned image; and a dot size modification unit coupled tothe shape distortion determination unit for modifying the aligned imageto generate a shape-corrected image based on the distortion measure. 20.The correction system of claim 19 wherein the distortion measureincludes a deformation radius representing the difference between theradius of a dot in the reference image and the radius of a correspondingdot in the aligned image.
 21. The correction system of claim 18 whereinthe space deformation correction unit further comprises: a directed edgedetection unit for receiving the shape-corrected image and generatingedges based thereon; and a interface detection unit coupled to thedirected edge detection unit for receiving the edges and based thereonfor generating interfaces; and a dot alignment unit coupled to theinterface detection unit for generating a corrected image based on theinterfaces and the shape-corrected image.